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A052812 A simple grammar: power set of pairs of sequences. 8
1, 0, 1, 2, 3, 6, 9, 16, 24, 42, 63, 102, 157, 244, 373, 570, 858, 1290, 1930, 2858, 4228, 6208, 9084, 13216, 19175, 27666, 39804, 57020, 81412, 115820, 164264, 232178, 327220, 459796, 644232, 900214, 1254554, 1743896, 2418071, 3344896, 4616026 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of partitions of n objects of two colors into distinct parts, where each part must contain at least one of each color. - Franklin T. Adams-Watters, Dec 28 2006

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 776

FORMULA

G.f.: exp(Sum((-1)^(j[1]+1)*(x^j[1])^2/(x^j[1]-1)^2/j[1], j[1]=1 .. infinity))

G.f.: Product_{k>=1} (1+x^k)^(k-1). - Vladeta Jovovic, Sep 17 2002

Weigh transform of b(n) = n-1. - Franklin T. Adams-Watters, Dec 28 2006

a(n) ~ Zeta(3)^(1/6) * exp(-Pi^4/(1296*Zeta(3)) - Pi^2 * n^(1/3) / (3^(4/3) * 2^(5/3) * Zeta(3)^(1/3)) + (3/2)^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (2^(1/4) * 3^(1/3) * n^(2/3) * sqrt(Pi)), where Zeta(3) = A002117. - Vaclav Kotesovec, Mar 07 2015

MAPLE

spec := [S, {B=Sequence(Z, 1 <= card), C=Prod(B, B), S= PowerSet(C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

MATHEMATICA

nmax=50; CoefficientList[Series[Product[(1+x^k)^(k-1), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 07 2015 *)

CROSSREFS

Cf. A026007, A052847, A219555, A255834, A255835.

Sequence in context: A147227 A147063 A007865 * A213331 A218153 A319642

Adjacent sequences:  A052809 A052810 A052811 * A052813 A052814 A052815

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

More terms from Vladeta Jovovic, Sep 17 2002

STATUS

approved

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)